Chứng minh đẳng thức: C n (k - 1) + C n k = C (n + 1) k
Chứng minh đẳng thức: Ck−1n+Ckn=Ckn+1.
Chứng minh đẳng thức: Ck−1n+Ckn=Ckn+1.
Ck−1n+Ckn=Ckn+1
=n!(k−1)!.[n−(k−1)]!+n!k!.(n−k)!
=n!(k−1)!(n−k+1)!+n!k!.(n−k)!
=n!k!.1k.(n−k)!.(n−k+1)+n!k!.(n−k)!
=n!.kn−k+1k!.(n−k)!+n!k!.(n−k)!
=n!k!.(n−k)!.(kn−k+1+1)
=n!k!.(n−k)!.(k+n−k+1n−k+1)
=n!k!.(n−k)!.(n+1n−k+1)
=(n+1)!k!.(n−k+1)!=(n+1)!k!.[(n+1)−k]!
=Ckn+1
Vậy Ck−1n+Ckn=Ckn+1.